This work considers which higher order modeling e ffects on the cosmic shear angular power spectra must be taken into account for Euclid. We identified the relevant terms and quantified their individual and cumulative impact on the cosmological parameter inferences from Euclid. We computed the values of these higher order e ffects using analytic expressions and calculated the impact on cosmological parameter estimations using the Fisher matrix formalism. We reviewed 24 effects and determined the ones that potentially need to be accounted for, namely: the reduced shear approximation, magnification bias, source-lens clustering, source obscuration, local Universe effects, and the flat Universe assumption. After computing these e ffects explicitly and calculating their cosmological parameter biases, using a maximum multipole of l = 5000, we find that the magnification bias, source-lens clustering, source obscuration, and local Universe terms individually produce significant ( >0 :25 sigma) cosmological biases in one or more parameters; accordingly, these e ffects must be accounted for and warrant further investigation. In total, we find biases in Omega(m), Omega(b), h, and sigma(8) of 0 :73 sigma, 0 :28 sigma, 0 :25 sigma, and 0 :79 sigma, respectively, for the flat Lambda CDM. For the w(0)w(a)CDM case, we found biases in Omega(m), Omega(b), h, ns, sigma(8), and w(a) of 1 :49 sigma, 0 :35 sigma, 1 :36 sigma, 1 :31 sigma, 0 :84 sigma, and 0 :35 sigma, respectively. These are increased relative to the Lambda CDM due to additional degeneracies as a function of redshift and scale.